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PK/PD Modeling of Therapeutic Effects of Erythropoietin

PK/PD Modeling of Therapeutic Effects of Erythropoietin. Wojciech Krzyzanski, PhD, MA Department of Pharmaceutical Sciences University at Buffalo. Semiparametric Bayesian Inference: Applications in Pharmacokinetics and Pharmacodynamics SAMSI, Research Triangle Park, July 14 2010.

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PK/PD Modeling of Therapeutic Effects of Erythropoietin

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  1. PK/PD Modeling of Therapeutic Effects of Erythropoietin Wojciech Krzyzanski, PhD, MA Department of Pharmaceutical Sciences University at Buffalo Semiparametric Bayesian Inference: Applications in Pharmacokinetics and Pharmacodynamics SAMSI, Research Triangle Park, July 14 2010

  2. General Model of Hematopiesis From Kaushansky, N. Engl. J. Med. 354:2034 (2006).

  3. + Erythropoietin (EPO) pO2-dependent production Kidney Bone marrow Red blood cells (O2-capacity, arterial pO2) Regulation of Erythropoiesis Wolber and Jelkmann., News Physiol. Sci. 17: 6 (2002)

  4. Erythropoietin  EPO is a 30.4 kD glycoprotein responsible for survival, proliferation, and maturation of erythroid cells. EPO is produced by peritubal cells in the kidneys in response to tissue hypoxia. Indications for rHuEPO: -Anemia of chronic renal failure - Chemotherapy induced anemia - Anemia of prematurity

  5. Erythropoietin Receptor  EPOR is a 185 kD member of the class 1 cytokine receptor superfamily. Expressed on erythroid progenitor cells, epicardium, neurons, liver, gut, endothelium. Upon binding to EPO homodimerizes and activates JAK2 tyrosine kinase. EPO-EPOR complex is internalized and degraded by the endosome-lysosome pathway. KD ~ 100-200 pM Internalization rate ~ 0.7 h-1 300- 1000 receptors per erythroid cell Sawyer et al., JBC 262: 5554 (1987); Broudy et al., Blood 77: 2583 (1991)

  6. rHuEPO Pharmacokinetics 300 IU/kg 600 IU/kg 1200 IU/kg 2400 IU/kg 10000 1000 rHuEPO concentration (IU/l) 100 10 1 0 80 160 240 320 400 Time (hr) SC IV • Distribution: Vd = 3-5 L.  Moderate nonlinear clearance: t1/2 = 4-11 hr. •  Minimal renal and hepatic clearance. •  Receptor binding, internalization, and degradation in bone marrow. • Dose dependent bioavailability: F = 0.4-1. • Slow absorption from the injection site: flip-flop kinetics. Flaharty et al., Clin. Pharmacol. Ther. 47: 557-64 (1990). Ramakrishnan et al., J. Clin. Pharmacol. 44:991-1002 (2004).

  7. rHuEPO Pharmacodynamics rHuEPO was administered SC to healthy subjects 150 IU/kg t.i.w for four weeks. • rHuEPO pharmacodynamic responses • Reticuloctyte count • RBC • Hemoglobin concentration Krzyzanski et al., EJPS 26:295-306 (2005).

  8. PK/PD Modeling Paradigm Mager and Jusko, Clin. Pharmacol. Ther. 70:210-16 (2001).

  9. Receptor Mediated EPO Endocytosis and Degradation Gross and Lodish, J. Biol. Chem. 281:2024 (2006).

  10. Tissue DT ksyn kpt ktp kon DIV DPO, F•ka Ko, TINF Serum Cp Vc Free Receptor [Rmax-DR] Receptor Complex DR + koff kel kdeg km Target-Mediated Drug Disposition Mager and Jusko. J Pharmacokinet Pharmacodyn. 28:507-32 (2001)

  11. Stem Cell BFU-e CFU-e Proerythroblast Erythroblast EPOR- EPOR-/+ EPOR+++ EPOR+ EPOR+/- EPO responsive cells Reticulocyte EPOR- EPOR- RBC Erythropoietic Cascade

  12. Lifespan Distribution Cell lifespan - time a cell remains in the population Mean lifespan-population mean of the lifespan distribution

  13. Lifespan Controlled Cell Loss Point Lifespan Distribution: (t) = (t-TR) (kin* )(t) = kin(t-TR)

  14. Basic Model: Stimulation of kin Baseline: R0 = kin·TR Krzyzanski and Jusko, JPB 27: 467 (1999).

  15. PK/PD of rHuEPO in Rats Mean serum rHuEPO concentrations, reticulocyte, and hemoglobin levels following IV bolus administration of 10, 100, 450, 1350, and 4050 IU/kg in rats. Woo et al., JPP 34:849-68 (2007).

  16. TMDD PK/PD Model of rHuEPO Woo et al., JPP 34:849-68 (2007).

  17. PK/PD Model Equations Woo et al., JPP 34:849-68 (2007).

  18. PK/PD Model Equations Woo et al., JPP 34:849-68 (2007).

  19. Initial Conditions , for t < 0, and , for t  0 , for t  0 , for t  0 , for t  0 , for t  0 Woo et al., JPP 34:849-68 (2007).

  20. Baseline Equations Woo et al., JPP 34:849-68 (2007).

  21. Residual Error Variance Model Parameter estimates were obtained by minimizing the -2LL objective function in ADAPT II. Woo et al., JPP 34:849-68 (2007).

  22. Parameter Estimates Woo et al., JPP 34:849-68 (2007). a Parameter was fixed.

  23. Numerical Challenges • Stiffness: Receptor binding (kon, R0) is typically much faster than distribution and elimination (kel,ktp,kpt). • Delay differential equations: Lifespan based PD model requires a DDE solver.

  24. Parameter Estimability • Large number of model parameters. • Observable data (blood compartments) are poorly informative about processes occurring in the bone marrow: receptor binding, cell maturation, negative feedback. • Large values of SE of corresponding parameter estimates, correlations, singularity of covariance matrix. • Necessary reduction of the number of model parameters: - fixing at known physiological values. - simplifying assumptions: quasi steady-state etc.

  25. Conclusions • rHuEPO nonlinear PK can be explained by receptor mediated disposition. • PD response is significantly delayed with respect to PK exposure. • PK/PD model exhibits stiffness and requires DDE solver. • System large dimension and data based on blood measurements lead to parameter estimability problems.

  26. Acknowledgments • Sukyung Woo, PhD. • William Jusko, PhD.

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